An EGR system is effective for decreasing the amount of NO.sub.x in the exhaust gas since the combustion temperature in the combustion chambers of the engine is decreased by introducing recirculated gas into the combustion chambers. An air injection system is effective for decreasing the amounts of HC and CO in the exhaust gas, since the injected air serves to oxidize the HC and CO components in the catalytic converter. Therefore, in order to effectively decrease the three major toxic components, i.e. HC, CO and NO.sub.x, an internal combustion engine of a type provided with both an EGR system and an air injection system has also been proposed in the prior art. In such type of engine, if a large amount of injected secondary air is mixed with the exhaust gas to be recirculated, a combustible mixture from a carburetor of the engine becomes "lean", thereby causing an inferior EGR effect. This condition is due to the high temperature of the combustion of the "lean" mixture in the combustion chambers, which combustion generates a large amount of NO.sub.x components. Already provided in the prior art is an engine which prevents the mixing of injected secondary air with the exhaust gas to be recirculated. Such engine has an EGR system for recirculating exhaust gas, from at least one but not all of the combustion chambers into the intake manifold, and an air injection system for introducing secondary air into branch pipes connected to combustion chambers from which the exhaust gas is not recirculated. By the above-mentioned construction, the mixing of the injected air with the exhaust gas to be recirculated is prevented. Accordingly, the effect of decreasing NO.sub.x by utilizing the EGR operation as well as the effect of decreasing CO and HC by utilizing the air injection operation can be sufficiently attained.
However, in this type of internal combustion, since the secondary air is not introduced into all of the exhaust ports leading from the combustion chambers, oxidation of the HC and CO components does not occur at the exhaust ports, to which the secondary air is not introduced. Therefore, a low temperature of the exhaust gas directed toward the catalytic converter exists for a prolonged time after the cold start of the engine. Such low temperature causes the occurrence of an inferior operation in the catalytic converter. Consequently, a large amount of CO and HC components is emitted to the atmosphere without being cleaned during the warming-up condition of the engine.